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What is the smallest positive integer such that (98*k)^(1/3) is an integer

 Nov 30, 2020
 #1
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What is the smallest positive integer such that (98*k)^(1/3) is an integer

 

98 = 2 * 7^2

 

k =2^2  x  7 = 28

 Nov 30, 2020
 #2
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( 98 * k)^(1/3)  =

 

( 7^2 * 2 * k)^(1/3)

 

We need k  to be   7 * 2^2  =  28

 

Check  :    (98 * 28)^(1/3)  =  (2744)^(1/3)   =   14

 

cool cool cool

 Nov 30, 2020

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